climate change - 2 Flashcards
consider the case of stock pollution that has a relatively long life span but that are uniformly mixing, what are the two implications?
- Uniform mixing => pollutant concentrations will not differ from place to place; hence no spatial dimension is needed.
- Persistence of pollution stocks over time means that the temporal dimension is of utmost importance. Consequently we need to take into account the trajectory of emissions over time, instead of considering a single point.
GHG as a global pollutant has both of these properties.
what does a represent in the rate of change of pollutant stock model?
represents the proportion of At that decays, 0 < a < 1: hence the total amount of pollution decay equals aAt
a = 0 - there is no decay/perfectly persistent pollution
a = 1 - complete/instantaneous decay - the pollutant is basically a flow
a is independent of time
the stock in the case of perfectly persistent pollution
o Note: in the case of perfectly persistent pollution, the stock at any time isthe sum of all previous emissions. Hence, the pollution stock and pollution damages will continue to accumulate without bounds through time as long as M is positive and will last forever.
o Since the time-periods are linked together through stock-flow relationships, and that pollution lingers in the atmosphere for ever (e.g. GHG from our perspective/lifetime), the policy-maker’s objective is to maximise discounted net benefits over a certain time horizon by choosing a sequence of emission flows Mt for the period t = 0, to t = 1
Social/discount rate
Social (consumption)/ discount rate r shows the preference for for consumption in future periods.
d = 1/(1+r)
So, for r > 0, the future counts less for same quantity today. Hence higher is the value of r, less is the value of d -> less does the future count
The solution to the maximisation problem gives rise to the
Optimal trajectory - entire time-path of the emission level which usually consists of two parts: (i) steady-state where emissions (and concentration levels) remain constant throughout; and (ii) the adjustment phase - describes a path by which emissions move from the current level and eventually adjust to their efficient/steady-state levels
Characterisation of steady state conditions
- variables are constant over time
- At = 0
- an increase in a = a decrease in A
Interpretation of u
u is the shadow price of one unit of emission i.e. it is the marginal social value of a unit emission at the maximum social net benefit.
Since pollution is bad, the shadow price is negative, and -u is positive
dB/dM = dD/dA [1/(r+a)] - interpretation
Same as the efficiency condition: present value of benefit of a marginal unit of pollution = present value of loss (damage) of future net benefit that arises from the marginal unit of pollution. Note that since dD/dA lasts forever, to obtain the present value, we need to divide this by r and also a because of the on-going decay process. The “discount factor” 1=(r + a) has the effect of transforming the single period damage into its present-value equivalent.
dB/dM = dD/dA [1/(r+a)] - implications
All else equal, the faster the decay rate, the higher will be the efficient level of steady-state emission. Why?? Because for any given value of dD/dA, an increase in a -> the value of dB/dM would have to fall to satisfy the marginal equality and dB/dM decrease means higher emissions. i.e. greater value of a -> higher effective discount rate applied to the stock damage term and therefore smaller is its present value. A higher discount rate means we attach less weight to the future damages, hence emissions can be raised accordingly. Same implicationfor r : higher r means we attach less weight to damages to the future, andso the emission level can be raised accordingly.
Case when a = 0 (regardless of whether r>0 or r=0)
This means that the pollution is highly persistent, never decays! But then no steady state exists except for when M = 0 : the steady state cannot exist as for any positive value of M; A rises without bound.
Variable decay rate a
For example, the decay rate of GHG alters as the mean temperature levels change. Indeed, once they cross the threshold levels, the changes can become irreversible.
estimating extent of damages problem
So far, we have described our model by assuming that somehow we can estimate the extent of damages.But estimating the extent of damages in order to assess the impact of climate change itself is incredibly difficult! It involves the greatest uncertainties of all processes associated with global warming. It is compounded by the issues of measuring/estimating the discounting rate. What IS the true value of the discount factor?? How can we be certain about the expression that we use for the discount factor in order to assess the extent of damages? Tremendously difficult task! So estimating abatement costs is in fact quite simple compared to the estimating damages. Indeed, if damages can be estimated properly, then it is rather straightforward to come up with climate abatement costs/functions and relevant policies.
Integrated Assessment Models (IAMs)
IAMs are combined climate and economic models that allow a joint modelling of natural and socio-economic processes - primary analytical tool for quantitative policy analysis.
Elements of Integerated Assessment Models
- Projections of future emissions of a CO2 equivalent (CO2e) composite under”business as usual” (BAU), and one or another abatement scenario.
- Projections of future atmospheric concentration resulting from past, current, and future CO2 emissions.
- Projections of average global temperature changes.
- Projections of economic impact, usually expressed in terms of lost GDP and consumption resulting from higher temperature.
- Estimates of the cost of abating GHG emissions by various amounts, both now and throughout the future.
- Assumptions about social utility and the rate of time preference, so that lost consumption from expenditures on abatement can be valued and weighed against future consumption gains.
